On the location of critical points of polynomials
Authors:
Branko Curgus and Vania Mascioni
Journal:
Proc. Amer. Math. Soc. 131 (2003), 253264
MSC (2000):
Primary 30C15; Secondary 26C10
Published electronically:
June 3, 2002
MathSciNet review:
1929045
Fulltext PDF Free Access
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Abstract: Given a polynomial of degree and with at least two distinct roots let . For a fixed root we define the quantities and . We also define and to be the corresponding minima of and as runs over . Our main results show that the ratios and are bounded above and below by constants that only depend on the degree of . In particular, we prove that , for any polynomial of degree .
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 P. Henrici, Applied and computational complex analysis, Vol. 1, John Wiley & Sons, 1988. MR 90d:30002
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 J. L. Walsh, On the location of the roots of the derivative of a polynomial, C. R. Congr. Internat. des Mathématiciens, pp. 339342, Strasbourg, 1920.
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 J. L. Walsh, The location of critical points of analytic and harmonic functions, Amer. Math. Soc. Colloq. Publ., Vol. 34, 1950. MR 12:249d
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Additional Information
Branko Curgus
Affiliation:
Department of Mathematics, Western Washington University, Bellingham, Washington 98225
Email:
curgus@cc.wwu.edu
Vania Mascioni
Affiliation:
Department of Mathematics, Western Washington University, Bellingham, Washington 98225
Email:
masciov@cc.wwu.edu
DOI:
http://dx.doi.org/10.1090/S0002993902065346
PII:
S 00029939(02)065346
Keywords:
Roots of polynomials,
critical points of polynomials,
separation of roots
Received by editor(s):
July 10, 2001
Received by editor(s) in revised form:
September 4, 2001
Published electronically:
June 3, 2002
Communicated by:
N. TomczakJaegermann
Article copyright:
© Copyright 2002
American Mathematical Society
